\left. \begin{array} { l } { 3 \frac { 7 } { 10 } , 2 \frac { 4 } { 5 } , 3 \frac { 1 } { 4 } , 2 \frac { 3 } { 10 } , 3 \frac { 3 } { 4 } } \\ { 6 \frac { 9 } { 10 } , 7 \frac { 1 } { 5 } , 6 \frac { 3 } { 4 } , 7 \frac { 7 } { 10 } , 6 \frac { 4 } { 5 } } \end{array} \right.
Sort
\frac{23}{10},\frac{14}{5},\frac{13}{4},\frac{37}{10},\frac{15}{4},\frac{27}{4},\frac{34}{5},\frac{69}{10},\frac{36}{5},\frac{77}{10}
Evaluate
\frac{37}{10},\ \frac{14}{5},\ \frac{13}{4},\ \frac{23}{10},\ \frac{15}{4},\ \frac{69}{10},\ \frac{36}{5},\ \frac{27}{4},\ \frac{77}{10},\ \frac{34}{5}
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sort(\frac{30+7}{10},\frac{2\times 5+4}{5},\frac{3\times 4+1}{4},\frac{2\times 10+3}{10},\frac{3\times 4+3}{4},\frac{6\times 10+9}{10},\frac{7\times 5+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Multiply 3 and 10 to get 30.
sort(\frac{37}{10},\frac{2\times 5+4}{5},\frac{3\times 4+1}{4},\frac{2\times 10+3}{10},\frac{3\times 4+3}{4},\frac{6\times 10+9}{10},\frac{7\times 5+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Add 30 and 7 to get 37.
sort(\frac{37}{10},\frac{10+4}{5},\frac{3\times 4+1}{4},\frac{2\times 10+3}{10},\frac{3\times 4+3}{4},\frac{6\times 10+9}{10},\frac{7\times 5+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Multiply 2 and 5 to get 10.
sort(\frac{37}{10},\frac{14}{5},\frac{3\times 4+1}{4},\frac{2\times 10+3}{10},\frac{3\times 4+3}{4},\frac{6\times 10+9}{10},\frac{7\times 5+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Add 10 and 4 to get 14.
sort(\frac{37}{10},\frac{14}{5},\frac{12+1}{4},\frac{2\times 10+3}{10},\frac{3\times 4+3}{4},\frac{6\times 10+9}{10},\frac{7\times 5+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Multiply 3 and 4 to get 12.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{2\times 10+3}{10},\frac{3\times 4+3}{4},\frac{6\times 10+9}{10},\frac{7\times 5+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Add 12 and 1 to get 13.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{20+3}{10},\frac{3\times 4+3}{4},\frac{6\times 10+9}{10},\frac{7\times 5+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Multiply 2 and 10 to get 20.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{3\times 4+3}{4},\frac{6\times 10+9}{10},\frac{7\times 5+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Add 20 and 3 to get 23.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{12+3}{4},\frac{6\times 10+9}{10},\frac{7\times 5+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Multiply 3 and 4 to get 12.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4},\frac{6\times 10+9}{10},\frac{7\times 5+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Add 12 and 3 to get 15.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4},\frac{60+9}{10},\frac{7\times 5+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Multiply 6 and 10 to get 60.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4},\frac{69}{10},\frac{7\times 5+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Add 60 and 9 to get 69.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4},\frac{69}{10},\frac{35+1}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Multiply 7 and 5 to get 35.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4},\frac{69}{10},\frac{36}{5},\frac{6\times 4+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Add 35 and 1 to get 36.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4},\frac{69}{10},\frac{36}{5},\frac{24+3}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Multiply 6 and 4 to get 24.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4},\frac{69}{10},\frac{36}{5},\frac{27}{4},\frac{7\times 10+7}{10},\frac{6\times 5+4}{5})
Add 24 and 3 to get 27.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4},\frac{69}{10},\frac{36}{5},\frac{27}{4},\frac{70+7}{10},\frac{6\times 5+4}{5})
Multiply 7 and 10 to get 70.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4},\frac{69}{10},\frac{36}{5},\frac{27}{4},\frac{77}{10},\frac{6\times 5+4}{5})
Add 70 and 7 to get 77.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4},\frac{69}{10},\frac{36}{5},\frac{27}{4},\frac{77}{10},\frac{30+4}{5})
Multiply 6 and 5 to get 30.
sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4},\frac{69}{10},\frac{36}{5},\frac{27}{4},\frac{77}{10},\frac{34}{5})
Add 30 and 4 to get 34.
\frac{74}{20},\frac{56}{20},\frac{65}{20},\frac{46}{20},\frac{75}{20},\frac{138}{20},\frac{144}{20},\frac{135}{20},\frac{154}{20},\frac{136}{20}
Least common denominator of the numbers in the list \frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4},\frac{69}{10},\frac{36}{5},\frac{27}{4},\frac{77}{10},\frac{34}{5} is 20. Convert numbers in the list to fractions with denominator 20.
\frac{74}{20}
To sort the list, start from a single element \frac{74}{20}.
\frac{56}{20},\frac{74}{20}
Insert \frac{56}{20} to the appropriate location in the new list.
\frac{56}{20},\frac{65}{20},\frac{74}{20}
Insert \frac{65}{20} to the appropriate location in the new list.
\frac{46}{20},\frac{56}{20},\frac{65}{20},\frac{74}{20}
Insert \frac{46}{20} to the appropriate location in the new list.
\frac{46}{20},\frac{56}{20},\frac{65}{20},\frac{74}{20},\frac{75}{20}
Insert \frac{75}{20} to the appropriate location in the new list.
\frac{46}{20},\frac{56}{20},\frac{65}{20},\frac{74}{20},\frac{75}{20},\frac{138}{20}
Insert \frac{138}{20} to the appropriate location in the new list.
\frac{46}{20},\frac{56}{20},\frac{65}{20},\frac{74}{20},\frac{75}{20},\frac{138}{20},\frac{144}{20}
Insert \frac{144}{20} to the appropriate location in the new list.
\frac{46}{20},\frac{56}{20},\frac{65}{20},\frac{74}{20},\frac{75}{20},\frac{135}{20},\frac{138}{20},\frac{144}{20}
Insert \frac{135}{20} to the appropriate location in the new list.
\frac{46}{20},\frac{56}{20},\frac{65}{20},\frac{74}{20},\frac{75}{20},\frac{135}{20},\frac{138}{20},\frac{144}{20},\frac{154}{20}
Insert \frac{154}{20} to the appropriate location in the new list.
\frac{46}{20},\frac{56}{20},\frac{65}{20},\frac{74}{20},\frac{75}{20},\frac{135}{20},\frac{136}{20},\frac{138}{20},\frac{144}{20},\frac{154}{20}
Insert \frac{136}{20} to the appropriate location in the new list.
\frac{23}{10},\frac{14}{5},\frac{13}{4},\frac{37}{10},\frac{15}{4},\frac{27}{4},\frac{34}{5},\frac{69}{10},\frac{36}{5},\frac{77}{10}
Replace the obtained fractions with the initial values.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}